Cryptography Reference
In-Depth Information
the ordinary cube root of
x
. The eavesdropper needs no knowledge of the private decryp-
tion keys.
E
XAMPLE
.
Here we see this type of attack. You will be asked to program this in Java. We
will use
e
= 3, a small RSA encryption exponent. The private primes
p
1 and
q
1 for the first
recipient will be
p1 = 1797693134862315907729305190789024733617976978942306572734300811577
326758055009631327084773224075360211201138798713933576587897688144166224
928474306394741243777678934248654852763022196012460941194530829520850057
688381506823424628814739131105408272371633505106845862982399472459384797
16304835356329624224137859
q
1 = 3595386269724631815458610381578049467235953957884613145468601623154
653516110019262654169546448150720422402277597427867153175795376288332449
856948612789482487555357868497309705526044392024921882389061659041700115
376763013646849257629478262210816544743267010213691725964798944918769594
32609670712659248448276687
and so the public modulus of the first recipient is
n
1 = 6463401214262201460142975337733990392088820533943096806426069085504
931027773578178639440282304582692737743592184379603898823911830098184219
017630477289656624126175473460199218350039550077930421359211527676813513
655358443728523951232367618867695234094116329170407261008577515178308213
161721510479824786077168039180583408274776831691763152279716383800031412
340152137152869819345741269583108122123538437343928423821045606152759418
497127367645255205598014712084444888413036198687032378283647381146628192
392272381849431882332598356071136706057555737475784812146651136260498654
1276943834825366579731809108470421496863793133.
The private primes
p
2 and
q
2 of the second recipient will be
p
2 = 2876309015779705452366888305262439573788763166307690516374881298523
722812888015410123335637158520576337921822077942293722540636301030665959
885558890231585990044286294797847764420835513619937505911249327233360092
301410410917479406103582609768653235794613608170953380771839155935015675
460877365701273987586195643
q
2 = 2876309015779705452366888305262439573788763166307690516374881298523
722812888015410123335637158520576337921822077942293722540636301030665959
885558890231585990044286294797847764420835513619937505911249327233360092
301410410917479406103582609768653235794613608170953380771839155935015675
460877365701273987586198999
and so the public modulus of the second recipient is
n
2 = 8273153554255617868983008432299507701873690283447163912225368429446
311715550180068658483561349865846704311797996005892990494607142525675800
342567010930760478881504606029054999488050624099750939339790755426321297
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